MATHEMATICS WORKSHEET

[Pages:65]MATHEMATICS WORKSHEET

XI Grade (Semester 1)

Chapter 1

by : Ignatia Maria Midawati

SMAK ST. ALBERTUS (ST. ALBERT Senior High School)

Talang 1 Street Malang 65112, Indonesia Phone (0341) 564556, 581037 Fax.(0341) 552017 Email: sma@ homepage: , mathdempo. , mida39.

PREFACE

Mathematics Module "STATISTICS" is written for students of St. Albert Senior High School at XI Grade Semester 1.

The contents are arranged under some worksheets which the students can fill to learn Statistics. Each worksheet is expanded in detail and step by step manner for easy understanding. It starts with a brief introduction and explanation follwed by filled examples and numerous simple exercises to build up the student's technical skills and to reinforce his or her understanding.

It is hoped that this approach will enable the individual student working on his or her own to make effective use of the module besides enabling the teacher to use them with mixed ability groups.

Finally, we would like to thank to all those involved in the production of this module.

Ignatia Maria Midawati

CONTENTS

Page

Term in Mathematics - Statistics

3

Worksheet 1 ? Collecting & Organizing Data, Graphical representation ...................

4

Worksheet 2 ? Mean, Median, Quartile, and Mode of singular data ..........................

9

Worksheet 3 ? The Dispersion of Measurement of singular data ............................... 16

Worksheet 4 ? Frequency Distribution of grouped data .............................................

22

Worksheet 5 ? Measures of Central Tendency of grouped data .................................. 30

Worksheet 6 ? Cumulative Frequency Distribution ..................................................... 39

Worksheet 7 ? Median, Quartiles, and Percentiles ....................................................... 47

Worksheet 8 ? The Dispersion of Measurement of grouped data ................................. 57

First published July, 2008 2

TERM in MATHEMATICS

STATISTICS

NO Mathematics Expressions

1. 5 + 2 = 7

How to read in English Five plus two is equal to seven

2. 9 ? 3 = 6

Nine minus three is equal to six

3. 7 x 9 = 63

Seven times nine is equal to sixty three

4. 12 : 3 = 4

Twelve devided by three is equal to four

5. 1 , 1 24

6. 2 , 3 , 2 1 353

6. 2 , 3 , 2 1 353

7. a b

8 a>b

9. a b

10 a < b

11. a b

12. 34,528

13. 34.528 14. 450 15. 20 ? 30 16. 20 < x 30 17. 20 < x < 30 18. 20 < x < 30

a half , a quarter

Two thirds , three fifths , two and one third Two over three, three over five, two and one over three

Two over three, three over five, two and one over three a is not equal to b a is greater than b a is greater than or equal to b a is less than b a is less than or equal to b Thirty four thousands five hundred twenty eight Thirty four point five two eight Forty five degrees Interval twenty until thirty Twenty is less than x and x is less than or equal to thirty x is between twenty and thirty Twenty is less than x and x is less than thirty

3

Worksheet 1st

Topic : Collecting & Organizing Data, Graphical representation

TIME : 4 X 45 minutes

STANDARD COMPETENCY :

1. To use the rules of statistics, the rules of counting, and the properties of probability in problem solving.

BASIC COMPETENCY: 1.1 To read and present the data in a frequency table and bar chart, line chart, pie chart of

singular data with its interpretation.

In this chapter, you will learn : ? How to collect and organize data ? Graphical representation

Statistics is the branch of mathematics in which facts and information are collected, sorted, displayed, and analyzed. Statistics are used to make decisions and predict what may happen in the future.

A. Collecting and organizing data

DATA

Raw

Data

Frequency Tables

Graphical Representation

Data that have been collected but not organized in any way are called raw data. Raw data are difficult to interpret, so it can be arranged in a frequency table. A frequency table shows the number of times (frequency) each value occurs.

Tallying is a system of recording and counting results using diagonal lines grouped in fives. Each time five is reached, a horizontal line is drawn through the tally marks to make a group of five. The next line starts a new group.

B. Graphical representation

1. Pictograms A pictogram is a simple way of representing data. Frequency is indicated by identical pictures (called symbols or motifs) arranged rows or columns.

2. Bar graphs In bar charts or bar graphs, data are represented in a series of bars that are equally wide. The width itself is not significant, but all the bars should be the same width.

3. Pie charts (circle graph) A pie chart is a circle graph in which the angles of the sectors represent the frequency.

4

Example 1 The marks obtained by 50 students in a class test are given on the below. Make a frequency table for the given marks. Draw a bar graph to represent the data.

Raw data

10 3 6 4 7 7 4 5 6 9 4 8 6 7 5 5 6 7 5 4 6 5 6 9 1 8 2 3 4 1 7 5 4 6 7 6 4 5 6 8 7 5 6 1 6 5 4 6 7 7

Solution

Marks

Tally

1

2

3

4

5

6

7

8

9

10

Total number

Frequency

Example 2

Daily takings

Amount taken (dollars)

800 700 600 500 400 300 200 100

0 Mon Tue Wed Thu Fri Sat Day

5

This bar graph shows the takings of a small business. a. On which day was the

smallest amount of money collected? b. On which day was the largest amount of money collected? c. Find the total money collected for the week.

Solution

a. .................. ? it has the shortest bar. b. .................. ? it has the longest bar. c. The total money collected for the week = ........................................................

Example 3 Population of fallen out leaves 07.00 08.00 09.00 10.00 11.00 12.00

Look at the left pictogram. a. How many leaves are fallen out

at 10.00? b. How many leaves are the most

fallen? When?

Solution a. b.

Example 4 The table below shows how a student spends her day.

Activity No. of hours

School 8

Sleeping Homework

8

3

Show this on a pie chart!

Eating 1

Total no. of hours = ......

School

: ........

Sleeping

: ........

Homework

: ........

Eating

: ........

Other

: ........

Other 4

Solution

Activity Angle

School Sleeping Homework

Draw the pie chart! Label the graph and give it a title!

Eating

Other

6

Example 5 A person's expenditure each month is $1200, split as shown in the pie graph on the below. a. If the angle at the centre in the transport sector is 900, what amount of money is spent

on transport? b. If this person spends $700 on food, find the angle at the centre of this sector. c. What fraction of this person's expenditure is on clothing?

Food

Transport

900 Clothing

Solution

Exercise 1

1. A survey recorded the number of people living in each of 40 houses. The numbers were as follows:

3

4

2

4

3

2

2

5

4

3

4

1

2

6

3

5

5

2

4

1

4

3

4

2

4

4

6

2

4

3

2

5

4

5

6

4

2

3

2

4

a. Make a frequency table. b. Draw a bar graph to illustrate your results. c. What is the total number of people living in these 40 houses?

2. The table below shows how an income of $400 was spent. Show these data on a bar graph and a pie chart.

Amount

Food $120

Rent $80

Clothing Transport Savings

$40

$110

$50

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3. The pie chart on the right, which is not drawn to scale, shows the distribution of various types of land in a district. Calculate: a. the area of woodland as a fraction of the total area shown, b. the angle of the urban sector, c. the total area of the district.

Farmland

1500

Urban 50 km2

800 500 Woodland

Marsh

4.

A number of students were asked to name their favorite sport.

1 4

of the students

said tennis,

1 8

said

rugby,

1 3

said football and the rest said swimming.

a. What fraction said swimming?

b. Calculate the value of x, if x is the angle of the sector representing rugby in the

pie chart.

c. If 32 students chose football, how many said tennis?

5. The pie chart on the right, which is accurately drawn, shows the nationalities of people staying in a holiday hotel. a. Which of these five nationalities had the smallest number of people in the hotel? b. What fraction of the people in the hotel were French? Give the answer in its lowest terms. c. Write the answer to b). as a percentage correct to the nearest whole number. d. Write the ratio

number of Germans as a total number of people

decimal. e. If there were 288 people in the hotel

altogether, how many of them were Dutch?

Belgian Dutch

British

450

French

600

1350

German

6. Make a simple research of any data that you can collect in your daily life. Collect the data and make the frequency table and the charts.

7. Find a chart from any newspapers, make a conclusion from that chart.

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